Heretofore, in the technology of this art, Rene Descartes, in 1638, published the results of his mathematical investigation of aplanatic surfaces for refraction. These surfaces, first described by Descartes, are known as Cartesian optical surfaces abd meridian sections of the surfaces are known as Cartesian ovals. The Cartesian oval is a curve of 4th degree when the conjugate foci of the Cartesian optical surface are both finite. When one of the conjugate foci is at infinity, the Cartesian oval is a conic whose eccentricity e is equal to the ratio of the indices of refraction of the first and the second refracting medias respectively.
Raoul Fritz and Adrien Fritz were issued British Pat. No. 620,852, Contact Lenses, May 13, 1947. This patent describes a scleral contact lens in which the lens portion forms with the eye an aplanatic system.
George Butterfield was issued U.S. Pat. No. 2,544,246, Corneal Contact Lens, Mar. 6, 1951. This patent describes a contact lens having a spherical concave side with a central spherical optical zone of 5 mm diameter, surrounded by a series of spherical annular zones. FIG. 1 of the drawings of this patent shows all radii of curvature of the posterior concave surface including that of the central 5 mm spherical area, emanating from a single center of curvature located on the axis of the surface.
Noel O. Stimson was issued U.S. Pat. No. 2,653,515, Corneal Contact Lens, Sept. 29, 1953. This invention describes a corneal lens in which the concave posterior surface is toroidal, in which the concavity has a given radius in the horizontal meridian and a different radius, generally smaller, in the vertical meridian. The posterior concavity is provided with one or more discrete areas which extend out from the generally concave contour. The facets or protuberances constitute the only portion of the lens which actually contacts the cornea.
Daniel O. Elliot wrote a paper, "A Preliminary Report on Use of Gradient Ellipsoidal Curves Relative to Fitting of Contact Lenses", The Optometric Weekly, Vol. 55, No. 21, May 21, 1964. The concave surface of this lens has a spherical optical zone and is ground in spherical annular steps.
Charles W. Neefe was issued U.S. Pat. No. 3,187,338, Corneal Contact Lens Of Wide Fitting Range With Sine Curve Concave Surface, June 1, 1965. This patent describes a corneal contact lens having a concave surface of aspherical form from center to edge composed of a sine curve.
David Volk, the present applicant, in U.S. Pat. No. 3,218,765, Lens Generating Method, Nov. 23, 1965, first disclosed has definition of eccentricity as a differential equation, and further defined generalized or effective eccentricity of modified ellipsoids in terms of a Taylor series. Quoting from said patent, column 11, lines 35-46,
"In order to give a more exact description of the extended meridian profile of modified ellipsoids, eccentricity may be expressed in the form of a Taylor series. Using MacLaurin's formula, the eccentricity of modified ellipsoid can be written: ##EQU1## where e.sub.x given by (3) is defined as the generalized or effective eccentricity."
William Feinbloom was issued U.S. Pat. No. 3,227,507, Corneal Contact Lens Having Inner Ellipsoidal Surface, Jan. 4, 1966. The inner concave surface of the contact lenses of the Feinbloom patent has an optic zone area an inscribed sphere of radius r.sub.o. The spherical optic zone usually varies from 6 to 7.50 mm in diameter. The zone of inner surface beyond the central spherical optic zone may be an elliptical torus, or toric ellipsoid, or general ellipsoid, or some variation thereof, depending upon grinding and polishing procedures used.
David Volk, in U.S. Pat. No. 3,344,692, Method and Apparatus For Producing Aspheric Contact Lenses, Oct. 3, 1967, described the method and apparatus for producing aspheric contact lenses wich included the production of conicoids of revolution and modified conicoids of revolution having increasing eccentricity peripheralward from the apex of the lens surface and having decreasing eccentricity peripheralward from the apex of the lens surface.
David Volk, in U.S. Pat. No. 3,482,906, Dec. 9, 1969, Aspheric Corneal Contact Lens Series, defines the posterior corneal surfaces of the contact lenses of the lens series disclosed as conicoids of revolution including prolate ellipsoids, paraboloids and hyperboloids of two sheets, and shows the domain of the two parameters which define each lens in the series, apical radius of curvature and eccentricity.
David Volk, in U.S. Pat. No. 3,535,825, Method and Apparatus For Grinding and Polishing Aspheric Surfaces of Revolution, granted Oct. 27, 1970, amplified the concept of generalized or effective eccentricity by defining modified conicoids of revolution as hypereccentric, hypoeccentric and eccentric, and defining a family of isoeccentric surfaces which relates eccentric, hypereccentric and hypoeccentric surfaces.
David Volk, in U.S. Pat. No. 3,950,082, Ophthalmic Lens for Presbyopia and Aphakia, granted Apr. 13, 1976, defines eccentricity of a conic as a differential equation and again defines mathematically generalized or effective eccentricity of a modified conic in the form of a Taylor series.
David Volk, in U.S. Pat. No. 4,149,801, Method and Apparatus For Measuring Aspheric Contact Lens Surfaces, Apr. 17, 1979, describes a method and apparatus for determining eccentricity of conicoid of revolution contact lens surfaces at a given angular inclinations of the optical axis of the contact lens surface with respect to the optical axis of a contact lens measuring microscope. The method consists of measuring the principal radii of curvature about a given normal to the surface at a selected angle of inclination of the optical axis of the conicoid contact lens surface and utilizing the ratio of said two measured principal radii of curvature in a specific equation to determine the eccentricity of the surface.
In my U.S. Pat. No. 3,482,906, Aspheric Corneal Contact Lens Series, the aspheric surface of the contact lens of the invention is a conicoid of revolution as determined by two parameters within a two dimensional domain; apical radii of curvature ranging from 6.50 to 8.50 mm and eccentricity ranging from 0.4 to 1.6, see FIG. 1. The novel surface of the contact lens of this invention distinguishes from the prior art and in particular from the aforedescribed Volk invention of U.S. Pat. No. 3,482,906 by defining the aspheric surface of the lens of the present invention by at least three predetermined parameters: apical radius of curvature; apical eccentricity; and derivatives of eccentricity, i.e. one or more of the first, second, third, etc. derivatives of eccentricity, each derivative being a specific rate of change of eccentricity. Each of the three parameters is represented by a specific number or, when there is more than one derivative of eccentricity, a set of numbers for rates of change of eccentricity, each of which corresponds to a given derivative of eccentricity. FIG. 2 is a schematic representation of the three-dimensional domain or boundry whose coordinates represent the magnitudes of the parameters which define a novel aspheric surface of revolution of a lens of this invention.